login
Gaussian binomial coefficient [ n,4 ] for q = -3.
2

%I #23 Sep 08 2022 08:44:39

%S 1,61,5551,433771,35569222,2869444942,232740363922,18843459775162,

%T 1526550040078063,123644349019377043,10015359787639069513,

%U 811239619864365082573,65710531328480659504924

%N Gaussian binomial coefficient [ n,4 ] for q = -3.

%D J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

%H Vincenzo Librandi, <a href="/A015288/b015288.txt">Table of n, a(n) for n = 4..500</a>

%H <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (61,1830,-16470,-44469,59049).

%F G.f.: -x^4 / ( (x-1)*(27*x+1)*(81*x-1)*(9*x-1)*(3*x+1) ). - _R. J. Mathar_, Aug 03 2016

%t Table[QBinomial[n, 4, -3], {n, 4, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)

%o (Sage) [gaussian_binomial(n,4,-3) for n in range(4,17)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=4; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016

%K nonn,easy

%O 4,2

%A _Olivier GĂ©rard_, Dec 11 1999